A body of mass 2kg moving with a speed of 10m/s in the direction (3i+4j) collided with a second body B of mass 3kg moving with a velocity of (i+8j)m/s and they moved together after collision. Calculate their common velocity
conserve momentum.
m1*v1 + m2*v2 = (m1+m2)v
2(3i+4j) + 3(i+8j) = 5(xi+yj)
so you have
x = (2*3+3*1)/5
y = (2*4+3*8)/5
To solve this question, we can use the principles of conservation of momentum and apply them to the problem. The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Let's start by calculating the initial momentum of each object:
The momentum of the first body (A) can be calculated using the formula:
momentum_A = mass_A * velocity_A
Given that the mass of body A is 2 kg and the velocity is (3i + 4j) m/s, we can calculate the momentum:
momentum_A = 2 kg * (3i + 4j) m/s
= 6i kg*m/s + 8j kg*m/s
Similarly, the momentum of the second body (B) can be calculated using its mass and velocity:
momentum_B = mass_B * velocity_B
Given that the mass of body B is 3 kg and the velocity is (i + 8j) m/s, we can calculate the momentum:
momentum_B = 3 kg * (i + 8j) m/s
= 3i kg*m/s + 24j kg*m/s
Now, let's calculate the total initial momentum before the collision:
initial momentum = momentum_A + momentum_B
= (6i + 3i) kg*m/s + (8j + 24j) kg*m/s
= 9i kg*m/s + 32j kg*m/s
According to the conservation of momentum, the total initial momentum is equal to the total final momentum after the collision. Since the two objects stick together after the collision and move with a common velocity, we can represent their common velocity as (v, v) m/s.
Now, the final momentum of the combined body can be expressed as:
final momentum = total mass * common velocity
The total mass of the combined bodies is the sum of their individual masses:
total mass = mass_A + mass_B
= 2 kg + 3 kg
= 5 kg
Therefore, the final momentum is:
final momentum = 5 kg * (v, v) m/s
= (5v)i kg*m/s + (5v)j kg*m/s
According to the conservation of momentum, the initial and final momentum are equal. Hence, we can equate the two expressions for momentum:
9i kg*m/s + 32j kg*m/s = (5v)i kg*m/s + (5v)j kg*m/s
By comparing the i and j components, we can obtain two equations:
9 = 5v (for the i-component)
32 = 5v (for the j-component)
Solving these equations, we find that v = 9/5 = 1.8 m/s.
Therefore, the common velocity of the two bodies after the collision is (1.8, 1.8) m/s in the direction (i + j).